begin{tikzpicture}
    draw (0,0) circle (1cm);
    draw (2,-2)  circle (2cm);
end{tikzpicture}

begin{tikzpicture}
    tikzstyle{intersection} = [draw, circle ,fill=darkgray, inner sep=0.3mm]
    draw (0,0) arc (-90:70:1cm);
    draw (2,1.5)  arc (100:200:2cm);
end{tikzpicture}